Energy Scale Degradation in Sparse Quantum Solvers: A Barrier to Quantum Utility

• URL: http://arxiv.org/abs/2503.08303v1
• Date: Tue, 11 Mar 2025 11:14:05 GMT
• Title: Energy Scale Degradation in Sparse Quantum Solvers: A Barrier to Quantum Utility
• Authors: Thang N. Dinh, Cao P. Cong,
• Abstract summary: Quantum computing offers a promising route for tackling hard optimization problems by encoding them as Ising models.<n>Minor-embedding, mapping logical qubits onto chains of physical qubits, requires stronger intra-chain to maintain consistency.<n>This elevated coupling strength forces a rescaling of the Hamiltonian due to hardware-imposed limits on the allowable ranges of coupling strengths.<n>We show that as the connectivity degree increases, the effective temperature rises as a function, resulting in a success probability that decays exponentially.
• Score: 0.8340329709052821
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Quantum computing offers a promising route for tackling hard optimization problems by encoding them as Ising models. However, sparse qubit connectivity requires the use of minor-embedding, mapping logical qubits onto chains of physical qubits, which necessitates stronger intra-chain coupling to maintain consistency. This elevated coupling strength forces a rescaling of the Hamiltonian due to hardware-imposed limits on the allowable ranges of coupling strengths, reducing the energy gaps between competing states, thus, degrading the solver's performance. Here, we introduce a theoretical model that quantifies this degradation. We show that as the connectivity degree increases, the effective temperature rises as a polynomial function, resulting in a success probability that decays exponentially. Our analysis further establishes worst-case bounds on the energy scale degradation based on the inverse conductance of chain subgraphs, revealing two most important drivers of chain strength, \textit{chain volume} and \textit{chain connectivity}. Our findings indicate that achieving quantum advantage is inherently challenging. Experiments on D-Wave quantum annealers validate these findings, highlighting the need for hardware with improved connectivity and optimized scale-aware embedding algorithms.

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